Calculus and Its Applications, Brief Version (12th Ed.)
Brief Version

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Language: English
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For one-semester courses in Applied Calculus. 


Anticipating and meeting student needs

Calculus and Its Applications, Brief Version remains a best-selling text because of its intuitive approach that anticipates student needs, and a writing style that pairs clear explanations with carefully crafted figures to help students visualize concepts. Key enhancements in the 12th Edition include the earlier introduction of logarithmic and exponential functions to help students master these important functions and their applications. 


The text?s accompanying MyLab? Math course also has been revised substantially, as new co-author Gene Kramer (University of Cincinnati, Blue Ash) revisited every homework question and learning aid to improve  content clarity and accuracy. These and all other aspects of the new edition are designed to motivate and help students more readily understand and apply principles of calculus.


Note: The title of this text was formerly Calculus and Its Applications.


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Preface

Prerequisite Skills Diagnostic Test

R. Functions, Graphs, and Models

  • R.1 Graphs and Equations
  • R.2 Functions and Models
  • R.3 Finding Domain and Range
  • R.4 Slope and Linear Functions
  • R.5 Nonlinear Functions and Models
  • R.6 Exponential and Logarithmic Functions
  • R.7 Mathematical Modeling and Curve Fitting
  • Chapter Summary
  • Chapter Review Exercises
  • Chapter Test
  • Extended Technology Application: Average Price of a Movie Ticket

1. Differentiation

  • 1.1 Limits: A Numerical and Graphical Approach
  • 1.2 Algebraic Limits and Continuity
  • 1.3 Average Rates of Change
  • 1.4 Differentiation Using Limits and Difference Quotients
  • 1.5 Leibniz Notation and the Power and Sum—Difference Rules
  • 1.6 The Product and Quotient Rules
  • 1.7 The Chain Rule
  • 1.8 Higher-Order Derivatives
  • Chapter Summary
  • Chapter Review Exercises
  • Chapter Test
  • Extended Technology Application: Path of a Baseball: The Tale of the Tape

2. Exponential and Logarithmic Functions

  • 2.1 Exponential and Logarithmic Functions of the Natural Base, e
  • 2.2 Derivatives of Exponential (Base-e) Functions
  • 2.3 Derivatives of Natural Logarithmic Functions
  • 2.4 Applications: Uninhibited and Limited Growth Models
  • 2.5 Applications: Exponential Decay
  • 2.6 The Derivatives of ax and logax
  • Chapter Summary
  • Chapter Review Exercises
  • Chapter Test
  • Extended Technology Application: The Business of Motion Picture Revenue and DVD Release

3. Applications of Differentiation

  • 3.1 Using First Derivatives to Classify Maximum and Minimum Values and Sketch Graphs
  • 3.2 Using Second Derivatives to Classify Maximum and Minimum Values and Sketch Graphs
  • 3.3 Graph Sketching: Asymptotes and Rational Functions
  • 3.4 Optimization: Finding Absolute Maximum and Minimum Values
  • 3.5 Optimization: Business, Economics, and General Applications
  • 3.6 Marginals, Differentials, and Linearization
  • 3.7 Elasticity of Demand
  • 3.8 Implicit Differentiation and Logarithmic Differentiation
  • 3.9 Related Rates
  • Chapter Summary
  • Chapter Review Exercises
  • Chapter Test
  • Extended Technology Application: Maximum Sustainable Harvest

4. Integration

  • 4.1 Antidifferentiation
  • 4.2 Antiderivatives as Areas
  • 4.3 Area and Definite Integrals
  • 4.4 Properties of Definite Integrals: Additive Property, Average Value, and Moving Average
  • 4.5 Integration Techniques: Substitution
  • 4.6 Integration Techniques: Integration by Parts
  • 4.7 Numerical Integration
  • Chapter Summary
  • Chapter Review Exercises
  • Chapter Test
  • Extended Technology Application: Business and Economics: Distribution of Wealth

5. Applications of Integration

  • 5.1 Consumer and Producer Surplus; Price Floors, Price Ceilings, and Deadweight Loss
  • 5.2 Integrating Growth and Decay Models
  • 5.3 Improper Integrals
  • 5.4 Probability
  • 5.5 Probability: Expected Value; the Normal Distribution
  • 5.6 Volume
  • 5.7 Differential Equations
  • Chapter Summary
  • Chapter Review Exercises
  • Chapter Test
  • Extended Technology Application: Curve Fitting and Volumes of Containers

6. Functions of Several Variables

  • 6.1 Functions of Several Variables
  • 6.2 Partial Derivatives
  • 6.3 Maximum - Minimum Problems
  • 6.4 An Application: The Least-Squares Technique
  • 6.5 Constrained Optimization: Lagrange Multipliers and the Extreme-Value Theorem
  • 6.6 Double Integrals
  • Chapter Summary
  • Chapter Review Exercises
  • Chapter Test
  • Extended Technology Application: Minimizing Employees’ Travel Time in a Building

Cumulative Review

Appendices:

  • A: Review of Basic Algebra
  • B: Indeterminate Forms and l’Hôpital’s Rule
  • C: Regression and Microsoft Excel
  • D: Areas for a Standard Normal Distribution
  • E: Using Tables of Integration Formulas

Answers

Index of Applications

Index

About our authors

Marvin Bittinger has been teaching math at the university level for more than 38 years. Since 1968, he has been employed at Indiana University Purdue University Indianapolis, and is now professor emeritus of mathematics education. Professor Bittinger has authored over 250 publications on topics ranging from basic mathematics to algebra and trigonometry to applied calculus. He received his BA in mathematics from Manchester College and his PhD in mathematics education from Purdue University. Special honors include Distinguished Visiting Professor at the United States Air Force Academy and his election to the Manchester College Board of Trustees from 1992 to 1999. His hobbies include hiking in Utah, baseball, golf, and bowling. Professor Bittinger has also had the privilege of speaking at many mathematics conventions, most recently giving a lecture entitled "Baseball and Mathematics." In addition, he also has an interest in philosophy and theology, particularly apologetics. Professor Bittinger currently lives in Carmel, Indiana, with his wife, Elaine. He has 2 grown and married sons, Lowell and Chris, and 4 granddaughters.

David Ellenbogen has taught math at the college level for over 30 years, spending most of that time in the Massachusetts and Vermont community college systems, where he has served on both curriculum and developmental math committees. He has also taught at St. Michael's College and the University of Vermont. Professor Ellenbogen has been active in the American Mathematical Association of Two Year Colleges since 1985, having served on its Developmental Mathematics Committee and as a Vermont state delegate. He has been a member of the Mathematical Association of America since 1979, has authored dozens of publications on topics ranging from prealgebra to calculus, and has delivered lectures at numerous conferences on the use of language in mathematics. Professor Ellenbogen received hi

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